Problem: Divide. Write your answer in simplest form. $ \dfrac{1}{2} \div \left(-\dfrac{1}{7}\right) = {?} $
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $-\dfrac{1}{7}$ is $-\dfrac{7}{1}$. Therefore: $ \dfrac{1}{2} \div \left(-\dfrac{1}{7}\right) = \dfrac{1}{2} \times \left(-\dfrac{7}{1}\right) $ $ \phantom{\dfrac{1}{2} \div \left(-\dfrac{1}{7}\right)} = \dfrac{1 \times (-7)}{2 \times 1} $ $ \phantom{\dfrac{1}{2} \div \left(-\dfrac{1}{7}\right)} = -\dfrac{7}{2} $